Inexact regularized Newton method for unconstrained optimization with rapid rate of convergence
Abstract
This paper proposes an inexact regularized Newton method for solving unconstrained optimization problems. The proposed algorithm belongs to the class of outer-inner iteration scheme. Instead of solving exactly linear systems, iterative linear solver will be applied to find approximate search directions. We will show that the inexact algorithm preserved the fast local convergence property of exact algorithms. Some numerical experiments are also conducted to show the benefits of our proposed algorithm.